1. Technical Field
The present invention relates to coded modulation, and in particular, to systems and methods for rate adaptive coded-modulation based on irregular quasi-cyclic LDPC codes.
2. Description of the Related Art
As the response to never ending demands for higher data rates and distance independent connectivity, 100 Gb/s Ethernet (GbE) standard has been already adopted, and 400 GbE and 1 TbE have become the research focus of many researchers. IEEE ratified the 40/100 GbE standard IEEE 802.3ba in June 2010. The next upgrade on Ethernet to meet the ever-increasing capacity demands is likely to be 400 Gb/s. As the operating symbol rates increase, the deteriorating effects of fiber nonlinearities and polarization-mode dispersion (PMD) reach levels that inhibit reliable communication over the optical fiber network.
Thus solutions for 100 GbE and beyond need to attain ultra-high transmission speeds in terms of aggregate bit rates while keeping the operating symbol rates low to facilitate nonlinearity and PMD management, which may be accomplished by employing modulation formats with high spectral efficiencies (SE). However, as a signal constellation grows in size to increase its SE, so does the optical signal-to-noise ratio (OSNR) it needs to achieve a particular bit error ratio (BER), and this may be an issue in practice. When, on the other hand, used in combination with strong forward error correction (FEC) codes, the OSNR requirement of the systems employing such high-SE modulation formats may be significantly lowered. As a consequence, schemes that can combine modulation and coding, which are commonly referred to as coded modulation schemes, gain further importance in the design and implementation of high-speed optical communication systems. Furthermore, in the context of high-speed optical communication systems, the complexity of a coded modulation system also plays a crucial role. Thus, such schemes need to be designed meticulously to address both issues simultaneously and effectively.
One of the key enabling technologies for the next generation of optical transport is the soft decision Forward Error Correction (FEC). In particular, it has been shown that the Low Density Parity Check (LDPC) coded modulation based on large girth (e.g., ≧10) LDPC codes provides excellent Bit Error Rate (BER) performance. Unfortunately, the codeword lengths are excessively long for quasi-cyclic (QC) LDPC code design, and corresponding decoders are difficult to implement with currently existing hardware. Furthermore, large girth (e.g., girth-8) LDPC codes exhibit the error floor phenomenon. The error floor phenomenon is encountered in modern iterated sparse graph-based error correcting codes like LDPC codes and turbo codes. When the bit error ratio (BER) is plotted for conventional codes or for convolutional codes, the BER steadily decreases in the form of a curve as the Signal to Noise Ratio (SNR) condition becomes better. For LDPC codes and turbo codes, there exists a point after which the curve does not fall as quickly as before, in other words, there is a region in which performance flattens, and this region is called the error floor region.
Prior attempts to eliminate the error floor phenomenon have used an outer Binary Coded Hexadecimal/Reed-Solomon (BCH/RS) code, and by using this approach, the error floor of girth-8 and girth-6 LDPC codes can be effectively eliminated. However, a disadvantage of using this approach is that the corresponding net coding gains (NCGs) are much below that of large-girth LDPC codes.